Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
3 kgk = 210 N/m

A 3 kg mass on a spring with stiffness 210 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3 kgk = 210 N/m
f = Hz
2.Easy
0.8 kgk = 390 N/m

A 0.8 kg mass on a spring with stiffness 390 N/m oscillates on a frictionless surface. Find the period T.

m = 0.8 kgk = 390 N/m
T = s
3.Medium
L = 2.1 m

A simple pendulum has a length of 2.1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.1 mg = 9.81 m/s²
T = s
4.Medium
0.5 kgk = 280 N/mA = 13 cmx = 10 cm

A 0.5 kg mass on a spring with k = 280 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its speed v when it is 10 cm from equilibrium.

m = 0.5 kgk = 280 N/mA = 13 cmx = 10 cm
v = m/s
5.Hard
1.6 kgk = 190 N/mA = 9 cm

A 1.6 kg mass on a spring with k = 190 N/m is pulled 9 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.6 kgk = 190 N/mA = 9 cm
vmax = m/s
6.Hard
t (s)x (cm)t = ?9.6

A body oscillates in simple harmonic motion with period 3.2 s and amplitude 12 cm. What is the shortest time t it needs to move from its maximum displacement of 12 cm to a displacement of 9.6 cm?

T = 3.2 sA = 12 cmx = 9.6 cm
t = s

Answer key

  1. 1. f = 1.332 Hz
  2. 2. T = 0.2846 s
  3. 3. T = 2.907 s
  4. 4. v = 1.966 m/s
  5. 5. vmax = 0.9808 m/s
  6. 6. t = 0.3277 s

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